Adaptive Dynamics of Diverging Fitness Optima

Title : Adaptive Dynamics of Diverging Fitness Optima
SPAAM Seminar Series 2023/2024-Blaine van Rensburg (Birmingham)

We analyse a non-local parabolic integro-differential equation modelling the evolutionary dynamics of a phenotypically structured population in a changing environment. Such models arise in the study of species adapting to climate change, or cancer adapting to therapy. Our results concern the long-time behaviour, in the small mutation limit, of the model. The main novelty of our work is that the time- and trait-dependent per capita growth rate is characterised by having multiple (locally) optimal traits which shift at possibly different velocities. Our results imply that in populations undergoing competition in temporally changing environments, both the true optimal fitness and the required rate of adaptation for each of the diverging optimal traits contribute to the eventual dominance of one trait.

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